Contact Problems (eBook)

Editor's Preface; Biographical Sketch of L.A. Galin;
Chapter 1 A Review of Research before 1953; 1.1 Introduction; 1.2 Frictionless Plane Problems; 1.3 Plane Adhesive Contact Problems; 1.4 Plane Frictional Contact Problems; 1.5 Plane Contact between Two Elastic Bodies; 1.6 Three-Dimensional Contact Problems;
Chapter 2 Plane Elasticity Theory; 2.1 The Fundamental Equations; 2.2 Stresses and Displacements in a Semi-Infinite Elastic Plane;
Chapter 3 Plane Static Isotropic Contact Problems; 3.1 Boundary Conditions for Plane Contact Problems; 3.2 The Riemann-Hilbert Problem for the Half-Plane; 3.3 Frictionless Punch Problems - Introduction; 3.4 Frictionless Punch Problems - Theory; 3.5 Examples of Frictionless Problems; 3.6 Frictional Punch Problems - Theory; 3.7 Frictional Punch Problems - Examples; 3.8 Sliding Contact with Coulomb Friction; 3.9 A Two-Punch Problem;
Chapter 4 Moving Punches, and Anisotropic Media; 4.1 Introduction; 4.2 Dynamic Plane Isotropic Elasticity Theory; 4.3 Displacement - Stress Relations; 4.4 Boundary Value Problems for a Moving Punch; 4.5 Complex Variable Formulation for a Plane Anisotropic Elastic Body; 4.6 Contact Problems for an Anisotropic Half-Plane; 4.7 Stick-Slip Contact; 4.8 Contact of Two Elastic Bodies;
Chapter 5 Contact Problems in Three Dimensions; 5.1 The Papkovich-Neuber Solution; 5.2 Solutions of Laplace's Equation in Certain Curvilinear Coordinates; 5.3 Circular Punches; 5.4 The Green's Function for the Exterior of a Circular Disc; 5.5 Axisymmetric Frictionless Contact Problems; 5.6 Axisymmetric Contact with Prescribed Contact Region; 5.7 Loading Outside a Circular Punch; 5.8 Axi-Symmetric Contact Problems with Friction; 5.9 A Punch of Elliptic Cross-Section; 5.10 Forces and Moments on an Elliptical Punch; 5.11 A Punch of Arbitrary Cross-Section; 5.12 The Pressure of a Wedge-Shaped Punch with Plane Base; 5.13 A Slender Beam on an Elastic Body; 5.14 Contact of Two Elastic Bodies; 5.15 Contact between a Rigid Punch and a Clamped Plate;
Chapter 6 Viscoelasticity, Wear and Roughness; 6.1 Introduction; 6.2 The Laplace Transform; 6.3 2-D Orthotropic Viscoelastic Bodies; 6.4 Adhesive Contact for a Viscoelastic Half-Plane; 6.5 Viscoelastic Rolling Contact; 6.6 The Limiting Case of Rolling of a Cylinder on a Viscoelastic Base; 6.7 Contact Problems in the Presence of Wear; 6.8 Axisymmetric Contact Problems in the Presence of Wear; 6.9 Plane Contact Problems for Rough Elastic Bodies; 6.10 Contact Problems for Rough Axisymmetric Elastic Bodies; References; Index;
Development of Galin's Research in Contact Mechanics by I.G. Goryacheva; 1. Two-Dimensional Sliding Contact of Elastic Bodies; 1.1 Problem Formulation; 1.2 Contact Problem for a Cylinder; 1.3 Contact Problem for a Flat Punch;
2. Contact Problem with Partial Slip for the Inclined Punch with Rounded Edges; 2.1 Problem Formulation; 2.2 Contact Pressure Analysis; 2.3 Shear Stress Analysis; 2.4 Tensile Stress Analysis; 2.5 Results and Discussions; 2.6 Conclusions; 2.7 Appendix;
3. Three-Dimensional Sliding Contact of Elastic Bodies; 3.1 The Friction Law Has the Form ;3.2 The Friction Law Has the Form;
4. Periodic Contact Problem; 4.1 One-Level Model; 4.2 Principle of Localization; 4.3 System of Indenters of Various Heights; 4.4 Stress Field Analysis;
Hertz Type Contact Problems for Power-Law Shaped Bodies, by Feodor M. Borodich;1. Introduction; 1.1 Hertz Type Contact Problems for rigid Indenters; 1.2 Formulation of a Hertz Type Contact Problem;
2. Frictionless Axisymmetric Contact; 2.1 The Galin Solution for Frictionless Axisymmetric Contact; 2.2 The Sneddon Representation of the Galin solution; 2.3 The Galin Solution for Monomial Punches; 2.4 A Solution for Polynomial Punches;
3. Axisymmetric Contact Problems with Molecular Adhesion;
4. Adhesive (No-Slip) Axisymmetric Contact Problems;4.1 Two-Dimensional Problem for a Punch with Horizontal Base; 4.2 Axisymmetric Adhesive Contact Problems for Curved Punches; 4.3 The Mossakovskii Solution for Adhesive Contact; 4.4 Solution to the Problem for Punches of Monomial Shape;
5. Self-similar Contact Problems; 5.1 Similarity Transformations for Hertz Type Contact Problems;5.2 Punches Described by Homogeneous Functions; 5.3 Punches Described by Parametric-Homogeneous Functions;
6. Hardness Measurements and Depth-Sensing Techniques; 6.1 Brief History of Hardness Measurements; 6.2 Depth-Sensing Techniques; 6.3 Adhesive (No-Slip) Indentation; 6.4 Similarity Considerations of 3D Indentation;
Further Developments of Galin's Stick-Slip Problem by Olesya I. Zhupanska;1. Introduction;
2. The Stick-Slip Problem in Galin's Formulation; 2.1 Refinements of Galin's Solution; 2.2 Solution of the Galin Stick-Slip Problem Due to Antipov and Arutyunyan; 2.3 Solution to the Galin Stick-Slip Problem Due to Spence;
3. Extensions to the Stick-Slip Contact Problem; 3.1 Arbitrary Load; 3.2 A Periodic System of Punches; 3.3 Self-similarity Approach in Stick-Slip Contact Problems